5 20th Century US Employment 1900200019501925197550%25%75%
6 Operations Heritage Eli Whitney Taylor, Gilbreths & Ford Hawthorne ExperimentsWalter Shewhart & Ed DemingGeorge DantzigShingo & Ohno
7 Trends in P/OM E-business Agility Ethics SCM Mgt of technology OutsourcingGlobalization
8 Competitiveness, Strategy and Productivity Chapter 2
9 Mission Accomplished! Missions Strategies Quality Cost Flexibility Social responsibilityDeliverability
10 Strategy Development & Implementation SWOT analysisCritical success factorsStaffingIntegration of OM w/other activities
11 Strategic Fit Organization Environment Strengths Weaknesses Opportunities Threats
12 Productivity Mathematical & intuitive definitions Number of inputs UsefulnessFactors affecting
13 Compute the multifactor productivity measure for each of the weeks shown. What do the productivity figures suggest? Assume 40-hour weeks and an hourly wage of $12. Overhead is 1.5 times weekly labor cost. Material is $6 per pound.WeekOutput (units)WorkersMaterial (lbs)130,0006450233,6007470332,200460435,4008480
14 Strategic OM Decisions Product & service designCapacityProcess selection & layoutWork designLocationQualityInventoryMaintenanceSchedulingSupply chainsProjects
16 Production & sales planning Time HorizonsShort, medium, long-range horizonsDifferences in horizonsPlan the systemPlan the use of the system3 yearsNowLocation, new productsProduction & sales planningSchedulingOur focus3 months
18 How to Forecast Use subject matter knowledge Use graphical methods Select model(s)Gather dataForecastValidate
19 Features of Forecasts Accuracy Paradigm Horizon Aggregate Timely AccurateReliableAppropriate unitsParsimoniousDocumented
20 Qualitative/Judgment Forecasts Why use one?Data, time, arenaTechniquesJury of executive opinionSalesforce OpinionConsumer SurveyDelphi MethodNominal Group Technique
21 Time Series Observations over a fixed interval of time Components of time seriesTrendSeasonalityCyclesIrregular variationsRandom variation
22 Notes on Notation F = Forecast A = Actual (known demand) t+1 = next period, t = current periodA bar over something means “average” e.g.∑ = repeated addition (summation)X
23 Time Series Techniques Naïve MethodNote discrepancy from textMoving AverageExponential Smoothing
24 More Time Series Equations Exponential Smoothing (alternate version)Linear Trend
25 Depends, Inc. sells adult diapers Depends, Inc. sells adult diapers. Monthly sales for a seven month period were as follows.Month Sales (000 units)Feb 19Mar 18Apr 15May 20Jun 18Jul 22Aug 20Plot the dataForecast sales for September using linear trend; 5 month moving average; exponential smoothing with alpha=0.2 assuming a July forecast of 19; naïve approach; weighted average of .60 for Aug, .30 for July, and .10 for June.
26 Seasonal Data Deseasonalizing alternatives A tourist center is open on weekends. The manager hopes to improve scheduling of part-time employees by developing a forecasting model. He assigns you this task but will ultimately take credit for your model.123456Friday149154152150159163Saturday250255260268273276Sunday166162171173176183
27 Associative Forecasting One item’s value depends on another item’s valueLinear regression
28 The following data were collected during a study of consumer buying patterns. Observation X Y Observation X YPlot the data.Obtain a regression line. How much variance is explained?Predict Y when X=41.
30 Accuracy & Control MAD = Mean Absolute Deviation Tracking Signal = MSE = Mean squared error
31 Doug Moodie is the president of Garden Products Limited Doug Moodie is the president of Garden Products Limited. Over the last 5 years, he has asked his vice president of marketing and his vice president of operations to provide sales forecasts. The actual sales and the forecasts are given here. Which vice president is better at forecasting?YearSalesVP MktVP Ops1167,325170,000160,0002175,362165,0003172,536180,0004156,732175,0005176,325
37 Service Blueprinting Physical Evidence Customer Onstage Service Backstage ServiceSupportLine of InteractionLine of Visibility
38 Quality Function Deployment A structured and disciplined process that provides a means to identify and carry the voice of the customer through each stage of product or service development and implementationQFD is:CommunicationDocumentationAnalysisPrioritizationQFD is a structured and disciplined process that takes time.QFD uses customer input to develop, implement, and improve a product/service.QFD improves communication in the following ways:The organization acts to understand its external customer.Vertical departments are involved in the design and development of products and services.QFD provides a team structure, which improves communication among team members.The QFD team and management communicate in a structured, documented fashion.The QFD matrices provide a detailed project tracking system that incorporates the QFD team’s consensus thinking process.The matrices provide a structured approach to analyze & prioritize inputbreakthroughs
39 Japanese QFD Results Design time reduced by ¼ to ½ Problems with initial quality decreasedComparison and analysis of competitive products became possibleCommunication between divisions improvedDesign time was reduced by one third to one half based on a study by Yoji Akao for JUSE in Reference Better Designs in Half the Time by Bob King, page 1-3, edition 3.0.Companies using QFD found a decrease in product/service problems related to design because QFD focused the organization on capability-driven designs.The Quality Characteristics/Demanded Quality (QC/DQ) chart provides a section to benchmark the organization against its competitors based on the voice of the customer.Communication between organizational units improved because each organizational unit was a part of the QFD team and spoke based on facts and the voice of the customer.
40 Product Design Time Line definitiondesignredesignoldsystemnewsystemThe old system created products with a design often based on the voice of the engineer. It is often called “folklore” design because it is guided by intuition. The end result is products sent to manufacturing that do not met process requirements, which causes continuous redesign and a wall placed between design and production and production and customer service. The method behind “folklore” design is “fire, ready, aim.”The new system is based on a marketing approach that factually understands the customer’s needs and expectations. By expanding the time taken to define the product, QFD virtually eliminates the need for redesign, especially on the critical items. Better documentation, improved communication, and a focus on priorities improves the efficiency of the initial design and significantly reduces the need for redesign.
41 Quality Function Deployment (in 75 minutes or less) Smylie Cellphone is a one-product company founded in Its product is a cell phone. The company’s annual sales last year were $18 million all in the United States. The company is located in Edmond in its own 400 square foot manufacturing plant and has 4 employees.The company recently completed a five-year business plan with a goal of expanding from a one-product to a multi-product line. The plan is to expand sales by attracting new customers and penetrating foreign markets. The company wants to develop a new cell phone that will appeal to adults in both the United States and foreign markets.Smylie Cellphone has selected your team to provide quality function deployment consulting services to help develop the new product. Your team has agreed as a first phase to develop chart A-1 detailing the following:1.Voice of the customer2. Degree of importance3. Company now and competitive comparison4. Company plan5. Improvement ratio6. Sales point7. Importance weight8. Relative weight9. Graphical competitive comparison10. Quality characteristics11. Relationships12. Importance weight13. Relative weight14. Technical comparison15. Special requirements16. Correlation matrixThe study must be painstaking in detail, unerring in accuracy, and completed in one hour. To show its commitment the company has agreed to have a representative available throughout the period for clarification and consultation.11011234567891213141516
42 1. Voice of the customer - Identify all customer groups and collect accurate information about their wants and needs (restrict yourself to 10 needs given our time constraint)2. Degree of importance - Identify the relative priority of each customer requirement using customer input to determine the values wherever possible. Use a scale of one to ten with ten indicating very important items.3. Company now and competitive comparison - Rate your current product (use the worst looking wallet in your group - in the event of a dispute as to whose wallet looks the worst, the company representative’s decision is final) and two competitors products on a scale of one to five with five being the best.4. Company plan - Determine what level you plan to achieve for each customer requirement. Since WWW’s resources are finite, make your improvement decisions based on steps 2 and 3. That is, choose the most important items where you can gain a clear advantage over your competitors. Use a scale of one to five with five being best.5. Improvement ratio - Quantify the improvement planned for each customer requirement by dividing the value of the planned level by the current company rating.6. Sales point - Identify major and minor points (front-of-the-brochure claims) by using information in columns 2 and 4. Restrict yourself to only a few sales points (perhaps two major and a minor point since we have only ten customer demands). Indicate the major points with this symbol and the minor points with this symbol . The major points are worth 1.5 and minor points are worth 1.2.7. Importance weight - Quantify the importance of each customer requirement to your company with the following equation: Importance weight = (column 2) x (column 5) x (column 6).8. Relative weight - Find the relative importance of each item in column 7 by summing column 7 and dividing each entry by the total. Express this as a percentage.9. Graphical competitive comparison - Plot the information in column 3 using a different symbol for the company and two competitors. This provides a comparison at a glance between the competitors rather than forcing the analyst to hunt for information in the matrix.10. Quality characteristics - Develop this list internally by looking at features of your current product, e.g., the stitching, type of leather, etc.11. Relationships - Identify all relationships that quality characteristics (column 10) have on voice of the customer items (column 1). Evaluate each pair by asking if the quality characteristic in any way affects the customer demanded quality item. Indicate the strengths of relationships by using the symbols , , and for strong (9), moderate (3), and weak (1) relationships respectively. Do not expect to find relationships between every pair of requirements.12. Importance weight - Quantify the importance of each technical requirement by multiplying the value of any relationships shown in the column of the technical requirement times the relative weight of the customer requirement.13. Relative weight - Similar to column 8 except you total the importance weights from row 12 and divide the weight of each item by the total. Express this as a percentage.14. Technical comparison - Identify how well you and your competitors fulfill each of the technical requirements using the same symbols and scale as in column 9.15. Special requirements - Identify any components governed by external sources, such as FDA, UL, etc. rules.16. Correlation matrix - Compare quality characteristics against each other to identify complementary or conflicting relationships early in the design process. Use the symbols and for strong and some positive correlation and x and for some and strong negative correlation respectively.
45 Reliability Probability Failure Normal operating conditions (remember Taguchi)Redundancy
46 Failure RatesProduct failure rate (FR) expressed in terms of time FR(N) or fraction of items tested FR(%)
47 Physio-Control burns-in their defibrillators for 24 hours after they are assembled. Over the past week they have produced 300 LifePak 12s. One unit failed on the first charge discharge cycle. Compute the failure rates and mean time between failures.
48 Reliability Calculations Two items that both must work for the system to perform are said to be in series0.950.90=
49 Backups (Redundancy) = These two components form a parallel subsystem that improves reliability0.800.700.95=
50 One of the industrial robots designed by a leading producer of servomechanisms has four major components. Components’ reliabilities are .98, .95, .94, and .90. All components must function in order for the robot to operate effectively.What is the robot’s reliability?If one backup can be added, where should it be?If one 0.92 backup can be added, where should it be?
51 MTBF/TF & the BathtubProduct failure is described as f(t)=λe-λt and when the slope of this cumulative failure curve is plotted, we get a bathtub shaped curve.Failure RateTime
52 Mean Time Between Failure Calculations P(no failure before T) = e -(T/MTBF)where:e is (and a calculator button)T is a specified length of timeMTBF is the mean time between failures as determined by historical dataProbabilities working the way they do, what’s the probability of failure before T?
53 FOX intends to launch a satellite that will enhance reception of television programs everywhere and complete Rupert Murdoch’s plan for world domination. According to FOX engineers, the satellite will have a useful life of eight years (four times as long as a typical sitcom). Determine the probability that the satellite will:a. Last more than nine yearsb. Last less than twelve yearsc. Fail between years nine and twelve
57 A work center operates 2 shifts per day 5 days per week (8 hours per shift) and has 4 machines of equal capability. This is the effective capacity. If the work center has a system efficiency of 95%, what is the expected output in hours per week?
58 Adjusting CapacityLong TermShort TermOVER UNDER
60 You are considering opening a copy service in the University Center You are considering opening a copy service in the University Center. You estimate your fixed cost at $15,000 and the variable cost of each copy sold at $ You plan to sell at $0.05.What is the break-even point in dollars?What is the break-even point in units?
62 Decision Making Alternatives States of nature Likelihood Payoffs Criterion
63 Decision Making Under Certainty The most unexciting of the decision environments... Next year’s demandAlternative Low HighDo nothing $50* $60ExpandSubcontract*profit in thousands
64 Decision Making Under Risk Likelihoods of the states of nature can be assigned a probability of occurrence and the payoff for each outcome can be estimated.Expected Monetary Value (EMV) Criterion
65 Clay Whybark, a soft drink vendor at Hard Rock Café’s annual Rockfest, created a table of conditional values for the various stocking sizes and crowd sizes. With the probabilities of the crowd sizes as indicated, what’s the best stock size for Clay to get rich?Crowd SizeAlternative Big Average SmallLarge Stock $22*Average StockSmall StockProbability*additional profit in thousands
66 Decision Tree Analysis Circles show states of natureDecision Tree Analysis$22Squares represent decision pointsa$121-$2These lines represent alternatives12$14b$103$69c$8$4
67 An entrepreneur must decide on the size of a latte stand to construct An entrepreneur must decide on the size of a latte stand to construct. The manager has narrowed the choice down to two: large or small. If he builds large and experiences low demand he could grin and bear it ($200), lower prices ($225), or hire street performers to attract attention ($175). If he builds small and experiences high demand he could do nothing ($175), stay open longer hours ($225), improve processes ($250), or raise prices ($200). Building large for large demand has an expected payoff of $250 and building small for small demand has an expected payoff of $175. There is a 0.7 probability of high demand and 0.3 probability of low demand. What size stand should be constructed to slake the unquenchable thirst of caffeine addicts?
68 DMUR Expected payoff under certainty Expected value of perfect informationEVPI = EPUC - EMV
69 Four alternative manufacturing methods are being considered for a new product. Profitability, which depends on method of manufacture and level of consumer acceptance, is anticipated as shown here:Profit ($ Thousands from Product)Projected AcceptanceMethod Low Med High Very HighProbabilityWhich method is best?What’s the most the company should invest in analyzing the situation?
70 Decision Making Under Uncertainty Characterized by a complete lack of knowledge regarding the likelihood of occurrence for each state of natureMaximaxMaximinMinimax regretLaplace/equally likely
71 Very Favorable Average Unfavorable Build new plant $350,000 $240,000 Given the following conditional value table, determine the appropriate decision under uncertainty using:MaximaxMaximinMinimaxLaplaceVery FavorableAverageUnfavorableBuild new plant$350,000$240,000-$300,000Subcontract$90,000$180,000-$20,000Overtime$110,000-$10,000$60,000Do nothing$0
72 A firm produces a perishable food product at a cost of $10/case and sells it for $15. The firm considers possible demands of 100, 200, and 300 cases. If demand is less than production, the excess is discarded but if demand is more than production the firm will produce the shortfall at $18/case. If P(100)=.2, P(200)=.2 and P(300)=.6, how much should be produced?
73 A decision maker faced with four alternatives and four states of nature develops this payoff table. If the decision maker knows nothing about the chances of occurrence of each state of nature, what would reasonable decisions be?How do your conclusions change if these values represent costs instead of revenues?s1s2s3s4d1149105d21187d3d413
78 Layouts Product Process Fixed-position Combination Cellular Office RetailWarehouse
79 Group Technology Part families Setup time, transportation, congestion Service applications
80 Layout Considerations Material handlingInformation flowsEnvironment/aestheticsCapacityCosts
81 Assembly-line Balancing Cycle Time (CT)Operating TimeOutputOutput =Minimum # Stations =Task TimesCycle Time
82 Line Balancing Rules Obey precedence requirements Obey scheduling rule(s)Fill up as much time as possible at each stationCompute efficiency & balance delay (idle time) since you’ll probably have to defend your balance
83 Task Time Pred Z 30 -- Y 42 X 12 Z, Y W 6 V 48 U 24 T S 36 T, V R U, S Use this table to balance the line for an output of 320 units in an 8 hour work day. Create a precedence diagram and balance the line using the largest-process-time rule and the smallest-process-time rule. Work times are in seconds.TaskTimePredZ30--Y42X12Z, YW6V48U24TS36T, VRU, S
84 The Mach 10 is a one-person sailboat designed to be used in the ocean The Mach 10 is a one-person sailboat designed to be used in the ocean minutes are available each day to manufacture the Mach 10. The daily demand is 60 boats.Task (minutes) Followsa 1 -b 1 ac 2 ad 1 ce 3 cf 1 cg 1 d, e, fh 2 bI 1 g, hDraw the precedence diagram.Determine the percentage of idle time.
85 An assembly line with 30 activities is to be balanced An assembly line with 30 activities is to be balanced. The total amount of time to complete all 30 activities is 42 minutes. The longest activity takes 2.4 minutes and the shortest takes 0.3 minutes. The line will operate for 450 minutes per day.What are the maximum and minimum cycle times?What output rate will be achieved by each of those cycle times?Suppose this line is balanced using ten workstations and a finished product can be produced every 4.2 minutes.What is the production rate in units/day?What is the assembly line efficiency?
87 Registration at UCO has always been a time of emotion, commotion, and lines as students move among four stations as shown here students moved from paperwork station A to advising B, and 550 went directly from A to picking up class cards C. Graduate students proceeded from A to the Bursar D. Adjacent stations are 30’ apart.What is the load x distance of the layout shown?Provide an improved layout and compute its cost.ABCD--45055050350200750ABCD
88 Use the information in the grid to assign departments to a 3x3 office space. 12345678XAOXOOEAEXAAAAEOAAAAAE
90 Linear ProgrammingUsed when scarce resources are used by competing products.ObjectiveDecision variablesConstraintsParameters
91 Rotgut White Lightning Corn 1 2 Sugar 3 Jugs Hours I make two different kinds of moonshine to supplement my meager wages. Rotgut sells for $8 per jug and White Lightning, the premium brand, sells for $12/jug. Below is a list of ingredients for a batch of each type:RotgutWhite LightningCorn12Sugar3JugsHoursI have on hand the following:40 bushels corn, 70 pounds sugar, 50 jugs, and 72 hours (before the revenoors come to bust up my still)How much of each flavor should I make?
93 Model formulation Identify decision variables Write an objective functionIdentify all constraintsWrite constraints with all decision variables on the left side of an inequalitySolve it graphically, using Excel, or simplex
94 Graphical Solutions Work with only two decision variables Sketch axes Plot each constraint (pick (0,y) and (x,0))Identify feasible regionFind vertices of feasible regionEvaluate objective function
95 Solve the following problem graphically: Maximize Z = 4X + 6YSubject to X Y ≤ 85X + 4Y ≤ 20X,Y ≥ 0
96 The grand Valley Company, run by the J Motwani family, produces two products, bed mattresses and box springs. A prior contract requires that the firm produce at least 30 mattresses or box springs, in any combination per week. In addition, labor union agreements demand that stitching machines be kept running at least 40 hours per week, which is one production period. Each box spring takes 2 hours of stitching time, while each mattress takes one hour on a machine. Each mattress produced costs $20; each box spring costs $24.Write the objective function and constraints in canonical form.Solve graphically.
97 Linear Programming in Excel One of Excel’s useful features is the ability to solve linear programming problems (especially those beyond our graphical abilities).The feature is invoked by creating a spreadsheet containing the objective function and constraints, selecting Tools from the main menu, and Solver from the submenu
98 Here is an Excel version of the moonshine problem BCDEFG316244RotgutWhite Lightning52=D5*D3+C5*C3Profit67Corn1=D7*$D$5+C7*$C$5<=408Sugar=D8*$D$5+C8*$C$5709Jugs=D9*$D$5+C9*$C$55010Hours=D10*$D$5+C10*$C$572Here is an Excel version of the moonshine problemBCDEFG3$16.00$24.004RotgutWhite Lightning52$Profit67Corn1<=408Sugar10709Jugs50Hours72The top view shows formulas and the bottom view shows initial calculations.
99 Once the basic set of equations has been entered, launch Solver and fill in the dialog boxes with references to your sheet.Target cell - The objective function value (E52)Equal to - Choose max or min based on the problemBy changing cells - The decision variables (C52:D52)Subject to the constraints - Add all constraints one at a time by referencing their function values (e.g., the amount of corn used, E47 must be less than the amount of corn on hand, G47)Once all constraints have been entered, choose Options and check the boxes for Assume Linear Model and Assume Non-Negative.Finally, choose Solve and wait for Excel to work its magic
100 Solver Output ReportsAnswer Report - contains the basic answer to the problem and reveals which constraints had an impact on your situation.Sensitivity Report - tells you reduced costs and shadow pricesLimits Report - don’t bother asking for this one. We won’t use its information.
101 The value of the objective function at the optimal solution Microsoft Excel 11.0 Answer ReportWorksheet: [Moonshine.xls]FormulationReport Created: 10/2/2006 1:09:33 PMTarget Cell (Max)CellNameOriginal ValueFinal Value$E$5$Adjustable Cells$C$5Rotgut10$D$5White Lightning15ConstraintsCell ValueFormulaStatusSlack$E$10Hours65$E$10<=$G$10Not Binding7$E$7Corn40$E$7<=$G$7Binding$E$8Sugar60$E$8<=$G$8$E$9Jugs50$E$9<=$G$9The optimal values of the decision variablesA binding constraint is one that limits the value our objective function can assume. We use up all of our corn and jugs (we have no slack).If a constraint is not binding, then we have some left over (slack) when we implement the optimal solution. We have 10 pounds of sugar and 7 hours to spare.
102 Increases or decreases within these ranges will result in the same product mix (but a different objective function value).Microsoft Excel 11.0 Sensitivity ReportWorksheet: [Moonshine.xls]FormulationReport Created: 10/2/2006 1:09:33 PMAdjustable CellsFinalReducedObjectiveAllowableCellNameValueCostCoefficientIncreaseDecrease$C$5Rotgut101684$D$5White Lightning1524ConstraintsShadowConstraintPriceR.H. Side$E$10Hours65721E+307$E$7Corn40$E$8Sugar6070$E$9Jugs505A one unit in(de)crease in the original amount of corn available will in(de)crease our profit by this amountAmount of resource to be taken away for a non-binding constraint to become binding, or a binding constraint to become more so.Extra amount of resource needed for a binding constraint to become non-binding. Note that this doesn’t apply to non-binding constraints, hence the huge amounts indicated.
108 TECHNICAL APPROACHES Ergonomics Work Measurement ignorance historical datadirect time studypredetermined time studywork sampling
109 Direct Time Study Method Define tasksDetermine sample sizeTake measurementsRate performance
110 What sample size should be used: if there should be a .95 probability that the value of the sample mean is within 2 minutes, given that the standard deviation is 4 minutes?there should be a 90% chance that the sample mean has an error of 0.10 minutes or less when the variance is estimated as 0.50 minutes?
111 Direct Time Study Observed Cycle Time (OT) = average observed time Normal Time (NT) = OT x Performance Rating< 100% is slow> 100% is fastStandard Time (ST) = NT/(1- Allowance Factor)breaksfatiguedowntime
112 Work SamplingPercentage of time on a taskDefine taskSpy randomly
113 If a worker has times of 8.4, 8.6, 8.3, 8.5, 8.7, 8.5, a performance rating of 90%, what is the normal time? If the allowance factor is 15%, what is the standard time for this operation?
114 A part-time employee who rolls out dough balls at a pizza restaurant was observed over a 40 hour period for a work sampling study. During that time, she prepared 550 pieces of pizza dough. The analyst made 50 observations and found this employee not working four times. The overall performance rating was The allowance for the job is 15%. Based on these data, what is the standard time for preparing pizza dough?
115 Labor StandardsLabor Efficiency Variance measures the difference between expected and actual costs.
116 A trucking company’s labor standard is 320 miles/8 hour shift A trucking company’s labor standard is 320 miles/8 hour shift. Drivers logged 31,525 miles and recorded 822 hours of work. If drivers are compensated $15/hour, what is the labor efficiency variance? If the standard is lowered 10% what is the labor efficiency variance?
117 A farming conglomerate expects a four person hay crew to place 1,750 bales in the barn per day. The labor cost is $600 per day for a crew of four. In the past four days 8,100 bales have been harvested. Should the conglomerate be pleased with this level of output?
127 ANALYSES $ SITE Q SITE W SITE X VOLUME Locational cost volume (semi- breakeven)minimizes total costs in desired output rangeFactor rating methodcreates scores for sites based on factors & importance$SITE QSITE WSITE XVOLUME
128 Location Per Year Per Unit Fixed and variable costs for four potential plant sites are below:Enumclaw $100K $30Renton $150K $20Kent $200K $35Snoqualmie $250K $11Over what range of output is each alternative superior? If the anticipated output is 8,000 units per year, which location is best?Fixed VariableLocation Per Year Per Unit
130 ANALYSES Transportation Model Center of gravity & simple median models minimizes transportation costs using LPCenter of gravity & simple median modelsminimizes transportation costs using geometry
131 City X Y Hugo 9.2 3.5 Durant 7.3 2.5 Players 7.8 1.4 Blackwell 5.0 8.4 A chain of insurance firms in OK needs to locate a central office from which to conduct internal audits and other periodic reviews of its facilities. Each site, except for Players, will be visited three times a year by Carroll Fisher, who will drive from the central office. Players will be visited five times a year. What coordinates represent the distance-minimizing central location for this office? What other factors should be considered?CityXYHugo9.23.5Durant7.32.5Players7.81.4Blackwell5.08.4Waurika2.86.5Velma5.52.4Ardmore3.6Hooker3.88.5
161 Act Pred Time A -- 6 E B 4 7 F C 3 G C, E 10 D 2 H D, F BT Corp. would like to determine ES, EF, LS, LF and slack for each activity. The total project completion time and the critical path should also be determined. Activity times and predecessors are:ActPredTimeA--6EB47FC3GC, E10D2HD, F
162 Project Scheduling Activity starting & ending times Total & Free Slack ES ruleEF ruleLS ruleLF ruleTotal & Free Slack
163 Probabilistic Pert 3 Time Estimates Mean Standard deviation & variance OptimisticPessimisticMost likelyMeanStandard deviation & varianceZ-score
164 Probabilistic PERTGiven the sequence of activities with optimistic, most likely, and pessimistic times, determine the expected completion time of the project and the variance.What is the probability the project can be completed in 24 days or less?What deadline yields a 90% probability of finishing on time?4, 7, 106, 9, 137, 10, 13
165 Activity Pred a m b A -- 9 10 11 B 4 16 C D 5 8 The estimated times and immediate predecessors for the activities in a project at Caesar Douglas’s retinal scanning company are given in the table below. Assume that the activity times are independent.ActivityPredambA--91011B416CD58Calculate the expected time and variance for each activityWhat is the expected completion time of each path?What is the variance of each path?If the time to complete AC is normally distributed, what is the probability it will be finished in 22 weeks or less?If the time to complete BD is normally distributed, what is the probability it will be finished in 22 weeks or less?Why is the probability that the critical path will be finished in 22 weeks not necessarily the probability that the project will be finished in 22 weeks?
166 Project CrashingCrashing a project involves paying more money to complete a project more quickly.Since the critical path determines the length of a project, it makes sense to reduce the length of activities on the critical path.CP activities should be reduced until the project is reduced to the desired length or you are paying more per day than you save.If you have multiple CPs, they should be shortened simultaneously.
167 Crashing (Time/Cost Tradeoffs) Given the project specifications shown, how fast can the project be finished and how much will it cost?Act. Time Minimum $Cost/day PredecessorABC BD CE AF D, E
168 Determine the cheapest completion time and cost for this project if it has a fixed cost of $1000 per day.ACTIVITY REQ TIME MIN TIME $/DAY5 3,8 6,